The two-dimensional potential energy surfaces for the (X) over tilde (2)Pi and (A) over tilde (2)Sigma (+) states of the He . SH and Ne . SH complexes have been calculated using the restricted open-shell coupled cluster theory [RCCSD(T)] and the triple-zeta augmented correlation consistent polarized basis sets with an additional (3s3p2d2f1g) set of bond functions. In the case of the (A) over tilde (2)Sigma (+) state of Ne . SH the entire surface has also been developed using the quadruple-zeta basis set with bond functions as exploratory calculations demonstrated significant differences between the RCCSD(T) results obtained with the triple- and quadruple-zeta basis sets. These potentials are somewhat shallower and less anisotropic in comparison to the surfaces for the related He . OH and Ne . OH complexes. in contrast to He . OH and Ne . OH, we find that the linear Rg-SH (Rg=He,Ne) configurations are in all but one case lower in energy than the Rg-HS geometries Variational calculations of the bound rotation-vibration states have been performed using Hamiltonians that included the RCCSD(T) potentials. The calculated ground-vibrational-state dissociation energy, D-0, the frequency of the intermolecular stretching vibration, and the rotational constant are in very good agreement with the available experimental results for the (X) over tilde (2)Pi state of both Ne . SH and Ne . SD. The energies of rotation-vibration levels for the Ne . SH and Ne . SD complexes in the (A) over tilde (2)Sigma (+) state calculated using the triple- or quadruple-zeta potentials differ significantly, but agreement with the experimental rovibrational transition frequencies and rotational constants is very good regardless of which potential is used.